Hey all, understand the pain point here. This has been an issue on Shopify since the beginning. That’s the sole reason we built the Customer Fields app back in 2015-- to allow your customers to edit their own name and/or email.
You can accomplish this “edit account” functionality on the app’s Lite plan, or upgrade to Pro to collect additional customer information with a custom registration form, or post-registration on the customer account page.
To @NicoRi 's point about sharing customer data-- we get it, and that’s why we offer a thorough privacy policy for complete transparency on what we do with your customer’s data. (Short summary: We’re a “data controller” and don’t do anything with customer data, except allow you to manage it).